Thoroughly coat each side of your steak with 1 tsp salt and 1 tsp pepper (for a total of 2 tsp on each side) and let rest at room temperature for a few minutes.
Slice zucchini into quarters and coat with light oil and 1 tsp salt.
In a small bowl, add butter, garlic, Dijon mustard, paprika, parsley, thyme, cayenne, remaining 1 tsp black pepper, and remaining 1 tsp salt. Stir until combined.
Coat one side of your steak with the butter mixture and lay uncoated-side-down on a heated grill, along with your zucchini.
Cover and when butter has completely melted, about 3-5 minutes, flip and repeat by coating the other side. Repeat every 3-5 minutes, basting each side, until the steak has reached an internal temperature of 130F-140F for rare or medium rare. Remember to rotate zucchini so that all pieces have grill marks on each side.
Remove vegetables and steak from grill and let steak rest for at least 10 minutes covered in aluminum foil. Slice and serve with additional compound butter as desired!